本論文「模擬退火演算法」針對高密度分波多工器有高效率及全域最佳解的優點設計，其光譜之透射及反射特性曲線應用此法均有效地達成光學特性之要求。本設計程序集中於1550 nm之波段，亦可應用於任意光譜波段。
再者，敘述「模擬退火演算法」在計算機輔助電路設計最佳化理論，有關對稱雙頻帶寬頻微帶線濾波器，其特性至少可達500MHz寬頻以上，以此理論應用於雙頻帶微帶線濾波器之設計，不需事先電路佈局及全波模擬的優勢，基於最佳化演算法退火步驟調整傳輸線之特徵阻抗及電性長度值合成2.4 GHz及5.2 GHz單一輸入埠及單一輸出埠之雙頻濾波器，為設計良好之雙頻電路結構，可由一寬頻之帶通（BP）及窄頻帶拒（BS）或三個帶拒具有三個傳輸零點之雙特性行為諧振器（DBR）或步階阻抗諧振（SIR）之二次諧波之波段調整在頻譜上合成，所以在合成過程中先藉由二個短截線並聯之開路或短路諧振為基本架構，此乃寬頻帶通及窄頻帶拒暨雙特性行為諧振器之理論，爾後衍生出二截或三截之串列短截線之開路或短路步階阻抗諧振架構，分別計算二、三、四階濾波器其評價函數均幾乎收斂至零，並趨近理想濾波器特性曲線，達到全域最佳解，之後並藉由最佳化微調之優勢調整二階濾波器之連接傳輸線，使其達成匹配及高品質因數（Hi-Q）之設計，有關最佳化演算法、全波電磁模擬及實作之雙寬頻帶濾波器之插入、入射及反射損失特性曲線均十分逼近，同理，此法之濾波應用不只適用於2.4 GHz及5.2 GHz，同時亦可應用於任何其他雙頻帶之設計。
最後，由最佳化後之實驗結果去分析此一新穎雙頻帶微帶線濾波器之架構，藉由步階阻抗諧振理論，利用S參數及ABCD矩陣之雙埠網路去分析，串聯及並聯連續序列多種變化之合併出短路諧振器及開路諧振器，並推導出雙頻諧振器簡易設計公式控制傳輸極點、零點暨四個衰減頻帶並合成濾波器。基於饋入點及諧振頻率選擇，傳輸零點因此決定，再藉由控制諧振器的阻抗比值，則雙頻中心頻率因此可以決定，然後選擇阻抗值之大小來決定濾波器之裙擺特性、品質因數及頻寬之大小。有關各種步階阻抗諧振雙中心頻率之最大分離間隔及最大頻寬限制亦被討論，及更進一步，全域合成法亦被使用有關微型化之領域，十分簡易之架構，基於彎折步階阻抗諧振器可明顯地降低50%之佈局面積，藉由匹配理論提昇雙頻濾波器的效率，調整傳輸線之阻抗及電性長度可補償雙頻帶響應之優質，以及彎折電路之匹配並改善插入及反射損失。模擬及實作之實驗結果應用此法亦十分有效地完成高效能、低價格、體積小、製程簡單、易於維護之商業化優勢，顯現出本研究之學理明晰正確，甚具應用價值。

This method shows the superiority of high effectiveness and global optimized solutions designing DWDM filters by using the idea of simulated annealing algorithm. The spectral transmittance and reflectance curves of these filters applying this method all effectively achieve their desired optical performances. Although the design procedure is concentrated on 1550 nm band, in general, this method can be applied to arbitrary optical bands.
Then, we present a computer-aided circuit design procedure of simulated annealing algorithm to optimize multi-wideband microstrip line filters with symmetrical at least 500 MHz bandwidths respectively. This method demonstrates the superiority of designing microstrip line dual-band filters without previous circuit layout first and full wave simulations. The value of characteristic impedances and electrical lengths of transmission lines synthesizing 2.4 GHz and 5.2 GHz multi-band filters with a single input and a single output are adjusted to the annealing process by the optimization algorithm. For the fine multi-band circuit models, it is imperative that one wide-band band-pass (BP) filter is inserting into one narrow band band-stop (BS) filter or double behavior resonator (DBR) is the three band-stop responses with three transmission zeros or stepped impedance resonator (SIR) is controlling the second harmonic band to be the pass-band in the frequency domain. Therefore, the synthesized procedure is first operated two stubs in parallel with the opened or short circuit resonator and they are based on the wide BP & narrow BS and DBR theorems. Then, we develop a series of two or three stubs with the opened or short circuit resonator to be the SIR configurations. The merit functions almost converge to zero to calculate the second, third and fourth order filters respectively and approach the ideal filter curve and global optimized solutions. We also take the advantage of tuning the connected transmission line (TL) for the second order filter by optimized algorithm then we can get the matched and high quality factor (Hi-Q) design. The optimized algorithm, full wave simulation and fabricated of multi-band insertion, transmission and reflection loss of responses are almost the same. The method is applicable not only in 2.4 GHz and 5.2 GHz, but can be applied to any other multi-frequency bands.
Finally, based on previously experiment results, we also analyze and present a novel method of designing microstrip line multi-frequencies band filters by applying the SIR technology. Based on these stated topologies and optimal algorithm results, we derived the general design and synthesized equations to get a very efficient theoretical response. Here, we proposed new some simplifications and general fundamental equations based on transmission poles and zeros to synthesize multi-passband and the four attenuated bands. Utilizing the S-parameter and the ABCD parameters of a two-port network is for the analysis of short-circuited and open-circuited resonators with various combinations of series and shunt sequences. The transmission zeros are determined where we consider the feeding positions and resonance frequency then by controlling the impedance ratio of the resonators, both center frequencies of the two passbands are determined. Therefore, we can choose the impedance magnitude to design the skirt performance, Q factor, and bandwidth of the filters. The separated distance of two center frequencies and limit maximum bandwidth for all of the resonators are discussed. Moreover, a global synthesis approach is also discussed on miniaturization. A simplified architecture based on bent SIR offers the 50% area reduction of layout. Technology of matching circuit creates higher performance multi-band filter. We adjust impedance and electrical length of TL to compensate multi-band and bending for matches and highly improve the insertion and reflection loss. Simulation and measurement are performed to validate our method and are pretty matched. It shows that these filters applying these methods all effectively achieved desired high performances, resulted in a lower cost of multi-band filters and opened the way to commercial mass productions.

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